Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
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14718DE CENTRO GRAVIT. SOLID. tione quarta Apollonius demonſtrauit. Si igitur à ſingu-
lis horum circulorum, duo cylindri fiant;
unus quidem ad
baſis partes;
alter ad partes uerticis: inſcripta erit in co-
no ſolida quædam figura, &
altera circumſcripta ex cylin-
dris æqualem altitudinem habentibus conſtans;
quorum
unuſquiſque, qui in
100[Figure 100] figura inſcripta con-
tinetur æqualis eſt ei,
qui ab eodem fit cir-
culo in figura circũ-
ſcripta.
Itaque cylin
drus o p æqualis eſt
cylindro o n;
cylin-
drus r s cylĩdro r q;
cylindrus u x cylin-
dro u t cſt æqualis;

&
alii aliis ſimiliter.
quare conſtat circũ-
ſcriptam figuram ſu-
perare inſcriptam cy
lindro, cuius baſis eſt
circulus circa diametrum a c, &
axis d e. atque hic eſtmi-
nor ſolida magnitudine propoſita.
PROBLEMA III. PROPOSITIO XII.
Data coni portione, poteſt ſolida quædam
figura inſcribi, &
altera circumſcribi ex cylindri
portionibus æqualem altitudinem habentibus;
ita ut circumſcripta inſcriptam exuperet, magni
tudine, quæ minor ſit ſolida magnitudine pro-
poſita.

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